Question

One diameter of the circle circumscribing the rectangle ABCD is 4y= x + 7.
If the coordinates of A and B are (-3, 4) and (5, 4) respectively, find the equation of the circle.

Answer 1

Clearly, the centre of the circle lies on the line 4y = x+ 7
The circle passes through A(-3, 4) and B(5, 4) The slope of the segment joining A and B is zero.
Therefore, the slope of the perpendicular bsieetor of AB is not defined.
Hence, the perpendicular bisector of AB will be parallel to they-axis and will pass through
$(\frac{-3+5}{2},\frac{4+4}{2})=(1,4)$.
The equation of the perpendicular bisector is x=1.
The intersection point of the perpendicular bisector and 4y = x + 7 is (1, 2)
$\therefore$ Centre = (1, 2)
Radius $=\sqrt{(5-1{)}^2+(4-2{)}^2}=\sqrt{20}$
Hence, the requird equation of the
$x^2+y^2-2x-4y-15=0$